Put early exercise

I'd like to have more intuition about the put option early exercise.
I think I understand that there are cases when it makes sense to exercise a put option - nonetheless I do see people exercising their puts and to me this is not optimal.

So my understanding must be flawed - exercise makes sense only if the cash left (after the stock from the put exercise is bought back is liquidated) yields more than the time value of the option at exercise time

Most of the time I've seen it happen is when a position goes from far out of the money to deep in the money.

Also its worth noting that getting stock put to you is entirely random - I knew 2 guys who had the same naked put position of 10 contracts and one of them had 1 contract and the other had 5 contracts put to him on the same day. The Options Clearing house "decides" and then sends the info to the broker.

ps If you're asking cause you write naked puts - don't do it. Just use Covered Calls. While they have the same risk profile ... more retail investors get blown out cause of naked put writing then anything else ... talk to a customer service rep at any online broker and they will say the same thing.

In the case I am interested about, there is usually some stocks to cover the put, so I am not worried about delivery, nor cash issues if there is a residual stock position left.
And I know that the assignment process is random.

What I would like to know is why the put was exercised in the first place - why the put buyer decides to do that. Very often this is not a good idea to me, specially now with very low interest rates.

I (almost) never exercise any puts and at the same time I am regularly assigned. So I am wondering, what I am missing? Do you often (or sometimes) exercise your put and why?